The Bianconeri look set to spend big this summer on the back of their run to the final of last season's Champions League and have already completed a €32 million deal with Palermo for Paulo Dybala that could rise to €40m including add-ons and bonuses.
Allegri has admitted, though, that he is particularly keen on a new No.10 as well as an old-school centre-forward.
When asked by the La Gazzetta dello Sport if he likes Oscar, the Bianconeri boss replied: "Very much. He is one of those players who can make a difference in Europe.
"I like Oscar, but I also like Isco, Javier Pastore, Angel Di Maria, Toni Kroos - all the best players from the Champions League.
"And Mandzukic? There are not many centre-forwards in potential transfer circulation. Mandzukic, Gonzalo Higuain, a few others.
"Mandzukic is a good man for relaunching attacks."
However, Allegri insisted his interest in Mandzukic does not mean that the club would consider cashing in on Alvaro Morata, who had a fine first season in Italy following last summer's switch from Real Madrid.
Indeed, the former Milan coach says he holds the Spain international in the highest esteem and that the Old Lady must try to build a team around the 22-year-old striker and fellow forward Kingsley Coman.
"If we were to sell Alvaro, we'd pocket €70-€80 million," he added. "That's the current value of Morata.
"I believe that Juve must count on him and also Coman, another youngster of an exceptional level who only needs a little time to explode."